The ARGO-YBJ (Astrophysical Radiation Ground-based Observatory at YangBaJing) experiment is designed for very high energy $gamma$-astronomy and cosmic ray researches. Due to the full coverage of a large area ($5600 m^2$) with resistive plate chambers at a very high altitude (4300 m a.s.l.), the ARGO-YBJ detector is used to search for transient phenomena, such as Gamma-ray bursts (GRBs). Because the ARGO-YBJ detector has a large field of view ($sim$2 sr) and is operated with a high duty cycle ($>$90%), it is well suited for GRB surveying and can be operated in searches for high energy GRBs following alarms set by satellite-borne observations at lower energies. In this paper, the sensitivity of the ARGO-YBJ detector for GRB detection is estimated. Upper limits to fluence with 99% confidence level for 26 GRBs inside the field of view from June 2006 to January 2009 are set in the two energy ranges 10$-$100 GeV and 10 GeV$-$1 TeV.
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